---
title: "mlab-ops — Mova code model"
description: "Mova code model of mlab/src/ops.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/mlab/src/ops.rs.groupant/"
---
Elamur: [Mova](https://md.mova.elamur.ai/free/en/) · [Dictionary](https://md.dictionary.elamur.ai/free/en/) · [Research](https://md.research.elamur.ai/free/en/) · **Groupants**

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# mlab-ops

The groupant beside mlab/src/ops.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.

## Facts

- **kind:** groupant
- **status:** partial source bound model
- **source:** [`mlab/src/ops.rs`](https://github.com/ElamurAI/mova-free/blob/main/mlab/src/ops.rs)
- **source SHA-256:** `d0d25c3a91fa1ef8…`
- **repository folder:** [`mlab/src/ops.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/mlab/src/ops.rs.groupant)
- **repository commit:** `855da7bd4a7b`

> **Implementation material.** A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.

## Components

| component | label | where |
|---|---|---|
| **approximant** | partial | [approximant](#approximant) |
| **ast** | partial | `syntax.json` |
| **composition** | partial | [composition](#composition) |
| **cost** | symbolic source derived | [invariant](#invariant) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | executed bounded checks | [tests](#tests) |

## Obernants

The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.

| id | type | label | where |
|---|---|---|---|
| `behavior_complement` | behavior_complement | partial source derived model | [behavior_complement](#behavior-complement) |
| `reverse_reconstruction` | reverse_reconstruction | partial source derived model | [reverse_reconstruction](#reverse-reconstruction) |
| `representation_transport` | representation_transport | partial source derived model | [representation_transport](#representation-transport) |
| `failure_precedence` | failure_precedence | partial source derived model | [failure_precedence](#failure-precedence) |
| `resource_domain` | resource_domain | partial source derived model | [resource_domain](#resource-domain) |
| `interaction_relation` | interaction_relation | partial source derived model | [interaction_relation](#interaction-relation) |

## Parts

- [mlab-ops-broadcast](https://md.groupants.elamur.ai/free/en/mova/mlab/src/ops.rs.groupant/broadcast.groupant/)
- [mlab-ops-finite-range](https://md.groupants.elamur.ai/free/en/mova/mlab/src/ops.rs.groupant/finite-range.groupant/)

## Model text


### descriptant

#### Broadcast, matrix arithmetic and finite ranges

map2 uses equal-shape zip, then scalar fast paths, else singleton-dimension broadcast with k=(cols==1?0:j)*rows+(rows==1?0:i). matmul delegates scalars to EMul, checks inner dimensions, uses small loops or faer at m*n*k>=32768; complex large products combine four real products. range_spec computes n=floor((b-a)/s+3eps*max(abs(span),1))+1 with endpoint snapping and evaluates from nearer end. Concatenation discards empty pieces for shape matching, but includes classes in result class choice.

##### Modeling epoch 2026-10-31

Prospective source reading precedes test additions. Retained observations: parser distinguishes matrix and elementwise operators; interp owns short-circuit &&/|| rather than this binary entrypoint. value storage and index output shape determine broadcast. linalg owns solves/inverse; core colon delegates range while reshape preserves storage rather than transpose.

This is partial source-derived modeling, not proof, full semantic coverage, or a performance result. Public malformed representations, unbounded allocations and exhaustive numerical edge cases remain outside the checked fixtures.

### approximant

#### Broadcast, matrix arithmetic and finite ranges forward relation

map2 uses equal-shape zip, then scalar fast paths, else singleton-dimension broadcast with k=(cols==1?0:j)*rows+(rows==1?0:i). matmul delegates scalars to EMul, checks inner dimensions, uses small loops or faer at m*n*k>=32768; complex large products combine four real products. range_spec computes n=floor((b-a)/s+3eps*max(abs(span),1))+1 with endpoint snapping and evaluates from nearer end. Concatenation discards empty pieces for shape matching, but includes classes in result class choice.

Domain: Well-formed bounded Mat; finite modest range spans fitting usize count and memory; f64 overflow/NaN otherwise follows individual branch, no uniform numerical bound. Linalg callbacks can warn through Interp; no GPU required.

No executable Rust surrogate is supplied: categorical decisions require exact observations; numerical kernels have no measured approximation metric here. Future supported caps are 1%, 2%, 5%, 10% only.

### invariant

#### Invariant and cost

Arithmetic outputs double, comparisons/logical outputs logical; complex constructors narrow all-zero imaginary parts. truthy is nonempty and all complex elements nonzero. RangeSpec::at only modeled for k<n; dimension products/count conversion are unchecked. Scalar zero powers use cpow integer branch before zero-base fallback.

Cost: Broadcast O(output cells), small matmul O(mnk), matrix power O(log |p|) products plus inverse for negative p; large products delegate faer. Materialized range O(n), lazy at O(1). Concat allocates/clones linear total cells. No measured speed claim.

Failure ordering: binary handles strings before matrix extraction; left mat extraction before right; scalar division before shape/linalg. mpower scalar/scalar before square integer path. map2 equal shape/scalars before bshape rows then cols; range checks invalid direction/NaN/zero before count arithmetic.

### composition

#### Parent composition

parser distinguishes matrix and elementwise operators; interp owns short-circuit &&/|| rather than this binary entrypoint. value storage and index output shape determine broadcast. linalg owns solves/inverse; core colon delegates range while reshape preserves storage rather than transpose.

Scoped fragments are projections over exact byte intervals in this source; they share one parent syntax projection. Uncovered declarations and embedded checks remain parent modeled. binary handles strings before matrix extraction; left mat extraction before right; scalar division before shape/linalg. mpower scalar/scalar before square integer path. map2 equal shape/scalars before bshape rows then cols; range checks invalid direction/NaN/zero before count arithmetic.

The relation is source-derived and finite checks cannot establish complete correctness or a composition-wide numerical error bound.

### models

### behavior_complement

Bounded broadcast excludes incompatible nonsingleton dimensions and incorrect column-major ordering. Wrong-direction/zero-step/NaN ranges exclude elements. Small real matmul skips zero RHS coefficients, therefore does not guarantee dense IEEE NaN*0 propagation. Comparisons < <= > >= ignore imaginary parts; no mathematical complex order is claimed.

### reverse_reconstruction

Broadcast result preimage includes all operand shapes allowed by singleton expansion and values satisfying per-cell operator relation; addition admits many decompositions. Matmul preimages are factorization relations, nonunique with nullspaces. Range vectors constrain start/step/endpoint up to floating rounding and snapping; empty ranges have many causes.

### representation_transport

Arithmetic outputs double, comparisons/logical outputs logical; complex constructors narrow all-zero imaginary parts. truthy is nonempty and all complex elements nonzero. RangeSpec::at only modeled for k<n; dimension products/count conversion are unchecked. Scalar zero powers use cpow integer branch before zero-base fallback.

### failure_precedence

binary handles strings before matrix extraction; left mat extraction before right; scalar division before shape/linalg. mpower scalar/scalar before square integer path. map2 equal shape/scalars before bshape rows then cols; range checks invalid direction/NaN/zero before count arithmetic.

### resource_domain

Well-formed bounded Mat; finite modest range spans fitting usize count and memory; f64 overflow/NaN otherwise follows individual branch, no uniform numerical bound. Linalg callbacks can warn through Interp; no GPU required.

### interaction_relation

parser distinguishes matrix and elementwise operators; interp owns short-circuit &&/|| rather than this binary entrypoint. value storage and index output shape determine broadcast. linalg owns solves/inverse; core colon delegates range while reshape preserves storage rather than transpose.


### tests

#### Source-specific bounded evidence

`ops::wave30::arithmetic`: column-major broadcast, empty truth, small complex product, finite ranges, concat shape error, zero-skipping NaN behavior.

Seven named tests each passed twice debug and twice release on 2026-10-31, with actual named log lines sorted and identical across all four runs (28 selected successful executions). Each source has a compiled changed-assertion negative control; six runtime sources additionally have compiled production-body mutants that fail those unchanged tests. AST has representation evidence only. Every mutant is byte-restored and its positive test rerun. See `evidence.json` for this source's exact hash, mutation and exit statuses. External receipts retain full logs, command metadata, control records and prospective notes.

Unexecuted here: No large faer, solve/power, strings, nonfinite range resource execution. No corpus, GPU, live filesystem, timer or callback run. No broad Clippy claim; dependency/style checks were not repeated. Only appended test blocks were rustfmt-formatted; original production bytes are unchanged.